多样极小极大定理在零和动态对局问题(I)

Abstract

考虑一个两人零和动态对局上的极小极大问题。我们将极小极大定理以一个随机对局系统建立损失和获益的总值函数，并证明极小极大定理在某些条件下存在鞍值函数，导出这个动态对局系统存在一平衡点。本文举一个简易的例子，说明协议的对局运作下，说明这个动态对局的架构与极小极大定理的相互关系。 Considering a minimax problem to a two-person zero-sum dynamic game, we establish the total value function of game losses and gains in a stochastic game system. It could perform a minimax theorem. Moreover, we prove that minimax theorem is established by the stochastic space of their strategy spaces for the two-person zero-sum dynamic game under the law of motion. It is also established that the saddle value function exists under certain natural conditions so that the equilibrium point exists in this dynamic game system. A practical example could be employed to our framework in the context.